Thévenin's Theorem with dependent sources (AC Analysis)

Thévenin's Theorem is a lot work itself, how much more if we had to add dependent sources. The introduction of dependent sources complicates the calculation and process in solving for the thevenins impedance (Zth).

Having dependent source/s twitches the process of Thévenin's theorem. 

1. Determine Voc (Vth) the usual way
2. Determine Zth:
- Remove all independent sources
- Place an assumed value of voltage at the open circuit
- Determine the current supplied by the assumed voltage source
- Solve for Zth using the formula:
Zth = (Assumed Voltage) / (Current Supplied by the Voltage)

Solving for Vth was already discussed on our previous entries, the problem however is with solving for the required thevenins impedance. This is tricky but we will try our best to express and try to make it a brief easy to understand entry.

Suppose we have this circuit.

As stated, the first process in solving for Zth is by removing all independent sources. Also for the following figure, we already removed the load impedance.

Nicely done eh? Now we have to place an assumed value of voltage at the open circuit.  And determine the current supplied by the assumed voltage source. In this case it is Io.

Usually when solving for the current in any given element on a circuit. Mesh analysis is the way to go. However, we also should consider if there is a better route around. This is where all of our learnings in circuits come into play. 

If we already acquired the current supplied by the assumed voltage source, which we should be, we can now get the thevenins impedance (Zth) (finally) using this equation. 

And tadaa! Now we have our Zth and Vth (which is solved in orthodox manner). The equivalent circuit should now be. 

From this point, We can now easily calculate the voltage from a to b simply by using voltage division.

We still think that this method is of greater hassle, because you will have multiple solutions, minimum of three different approach (for Vth, Zth, Vload) in order to find the required value. Although it is efficient that we learn different approach in order to become flexible when faced with different kinds or circuits.

Good? news! This will be our last topic for midterms. There's too much work to do. We have to double time! We worked on this path, we must stay and continue to venture forward. To never give up no matter how many tries (T.T) we must take.